Potential method in the theory of thermoviscoelastic mixtures

In this article, the linear theory of binary thermoviscoelastic mixtures is considered and the basic boundary value problems (BVPs) of steady vibrations are investigated. Namely, the fundamental solution of the system of equations of steady vibrations is constructed explicitly and its basic properties are established. Green’s second and third identities are obtained and the uniqueness theorems for classical solutions of the internal and external basic BVPs of steady vibrations are proved. The surface and volume potentials are constructed and their basic properties are given. The determinants of symbolic matrices are calculated explicitly. The BVPs are reduced to the always solvable singular integral equations for which Fredholm’s theorems are valid. Finally, the existence theorems for classical solutions of the internal and external BVPs of steady vibrations are proved by the potential method and the theory of singular integral equations.     

High-order approximations of three-phase-lag heat conduction model: Some qualitative results

This article deals with some high-order approximations of the three-phase-lag heat transfer model aiming, at first, to identify the restrictions that make them well-posed consistence. Consequently, a first result about the uniqueness and continuous dependence of the solutions with respect to the given initial data and to the supply term is established for the related initial boundary value problems. Subsequently, to provide a more comprehensive analysis of the model, some further spatial decay results are established, this time conveniently relaxing the hypotheses about the delay times and the thermal conductivities. More precisely, a theorem of influence domain is proved for the wave propagating models and an exponential decaying estimate of Saint-Venant type is established for the diffusive models.     

莫尔应变圆极点法及应变极点特性研究

极点是根据单元体的应变状态在莫尔应变圆上做出的一个特殊点,通过极点可以获得任意平面的应变状态。为确定莫尔应变圆上的极点,提出了2种方法——平行线法和法线法。采用反证法分别验证了平行线法和法线法确定的应变极点的唯一性,采用几何作图法分别验证了平行线法和法线法确定的应变极点的可靠性。研究表明2种方法确定的应变极点位于莫尔应变圆的同一条直径上;应力极点与应变极点位于莫尔应力圆与应变圆组成的同心圆的半径上。莫尔应变圆极点法具有简便、准确的优点,避免了复杂的公式计算,是求解岩土工程中的稳定和变形问题及确定单元体复杂应变状态的优选方法。     

On a Theory of Thermoelastic Materials with a Double Porosity Structure

In this article, we use the Nunziato–Cowin theory of materials with voids to derive a theory of thermoelastic solids, which have a double porosity structure. The new theory is not based on Darcy's law. In the case of equilibrium, in contrast with the classical theory of elastic materials with double porosity, the porosity structure of the body is influenced by the displacement field. We prove the uniqueness of solutions by means of the logarithmic convexity arguments as well as the instability of solutions whenever the internal energy is not positive definite. Later, we use semigroup arguments to prove the existence of solutions in the case that the internal energy is positive. The deformation of an elastic space with a spherical cavity is investigated.     

一类二次系统极限环唯一性的证明

本文对系统ｄｘ／ｄｔ＝－ｙ＋δｘ＋ｌｘ２＋ｍｘｙ＋ｎｙ２，ｄｙ／ｄｔ＝ｘ（１＋ａｘ＋ｂｙ）的极限环唯，性提供一个判别方法，即若ｌ－ａδ＝０和δ（ｍ－ｂδ）＋ｎ＝０，则该系统的极限环最多有一个．     

一类非线性发展方程的Cauchy问题

研究了受迫ＫｄＶ－Ｂｕｒｇｅｒｓ方程Ｃａｕｃｈｙ问题解的唯一性,稳定性以及该问题解的ｂｌｏｗ－ｕｐ性质。     

可交换的整函数的唯一性

本文证明了如下定理：设f(z)=H(z)+sum from i=1 c_iexp(a_iP(z)),其中H(z)、P(z)均为多项式,P(z)为非常数,a_i(i=1,2,….n)为相互判别的非零有穷复数,c_i(i=1,2,…,n)为非零有穷复数．若g(z)为有穷级非常数整函数,且与f(z)可交换测g(z)或者为线性的,或者P(g)≡aP(f)+q ,其中 ａ为非零常数,q(z)为次数不超过deg(P(z))的多项式．     

几类常微分方程线性边值问题

利用上下解方法讨论了四阶非线性常微分方程的几类满足线性边界条件的边值问题解的存在性和惟一性;并通过格林函数、Shauder不动点定理严格证明了这几类边值问题解的存在性和惟一性。     

现代分析化学中的三线性成分模型

本文针对现代分析化学实际 ,有选择性地介绍了三相三道三线性成分模型 ,扼要地列举了其主要的三线性分解算法 ,讨论了立体阵的秩估计、三线性分解的唯一性等。     

四阶泛函微分方程周期解的存在性和全局吸引性

研究四阶泛函微分方程x^（4）（t）＋a1x^′′′（t）＋a2x^′′（t）＋a3x^′（t）＋a4x（t）＋g（t,x（t—τ））=p（t）的周期解问题．首先将该方程转变为四维的拟线性微分方程（组）,得到该方程存在唯一周期解的充分条件;然后通过选取适当的李雅普诺夫函数,推导方程任一解的全局吸引性,并进一步得到方程周期解的全局吸引性．最后,通过实例证实了本文结果的正确性．